Working Papers

We
solve a general class of dynamic rational-inattention problems
in which an agent repeatedly acquires costly information about
an evolving state and selects actions. The solution resembles
the choice rule in a dynamic logit model, but it is biased
towards an optimal default rule that depends only on the history
of actions, not on the realized state. We apply the general
solution to the study of (i) the status quo bias; (ii) inertia
in actions leading to lagged adjustments to shocks; and (iii)
the tradeoff between accuracy and delay in decision-making.

We
introduce a learning framework in which a principal seeks to
determine the ability of an agent by observing his performance
on an adaptive test consisting of a finite sequence of questions
or tasks. The principal assigns questions over time depending on
the agent’s past performance. The agent can affect the
informativeness of the question outcome by choosing a costless,
unobserved action. The probability of success at a question is
jointly determined by the agent’s ability and action which he
chooses strategically with the goal of being perceived as high
ability. We show through a series of examples that the
principal’s ability to learn can be affected (either positively
or negatively) by the strategic behavior of the agent. Our goal
is to examine whether more informative tasks can generate the
appropriate incentives to enhance learning. We show that this is
indeed the case and, in doing so, we extend a classic learning
result from statistics to our environment.

When
an agent chooses between prospects, noise in information
processing generates an effect akin to the winner’s curse.
Statistically unbiased perception systematically overvalues the
chosen action because it fails to account for the possibility
that noise is responsible for making the preferred action appear
to be optimal. The optimal perception patterns share key
features with prospect theory, namely, overweighting of small
probability events (and corresponding underweighting of high
probability events), status quo bias, and reference-dependent
S-shaped valuations. These biases arise to correct for the
winner’s curse effect.

Publications

We
study the effect of frequent trading opportunities and
categorization on pricing of a risky asset. Frequent
opportunities to trade can lead to large distortions in prices
if some agents forecast future prices using a simplified model
of the world that fails to distinguish between some states. In
the limit as the period length vanishes, these distortions take
a particular form: the price must be the same in any two states
that a positive mass of agents categorize together. Price
distortions therefore tend to be large when different agents
categorize states in different ways, even if each individual’s
categorization is not very coarse. Supplementary Appendix

We
present a two-stage coordination game in which early choices of
experts with special interests are observed by followers who
move in the second stage. We show that the equilibrium outcome
is biased toward the experts’ interests even though followers
know the distribution of expert interests and account for it
when evaluating observed experts’ actions. Expert influence is
fully decentralized in the sense that each individual expert has
a negligible impact. The bias in favor of experts results from a
social learning effect that is multiplied through a coordination
motive. We show that the total effect can be large even if the
direct social learning effect is small. We apply our results to
the diffusion of products with network externalities and the
onset of social movements.

We
study coordination in dynamic global games with private
learning. Players choose whether and when to invest irreversibly
in a project whose success depends on its quality and the timing
of investment. Players gradually learn about project quality. We
identify conditions on temporal incentives under which, in
sufficiently long games, players coordinate on investing
whenever doing so is not dominated. Roughly speaking, this
outcome occurs whenever players' payoffs are sufficiently
tolerant of non-simultaneous coordination. We also identify
conditions under which players coordinate on the risk-dominant
action. We provide foundations for these results in terms of
higher order beliefs.

This
paper considers the problem of testing an expert who makes
probabilistic forecasts about the outcomes of a stochastic
process. I show that, as long as uninformed experts do not learn
the correct forecasts too quickly, a likelihood test can
distinguish informed from uninformed experts with high prior
probability. The test rejects informed experts on some
data-generating processes; however, the set of such processes is
topologically small. These results contrast sharply with many
negative results in the literature.

We
study the effects of stochastically delayed communication on
common knowledge acquisition (common learning). If messages do
not report dispatch times, communication prevents common
learning under general conditions even if common knowledge is
acquired without communication. If messages report dispatch
times, communication can destroy common learning under more
restrictive conditions. The failure of common learning in the
two cases is based on different infection arguments.
Communication can destroy common learning even if it ends in
finite time, or if agents communicate all of their information.
We also identify conditions under which common learning is
preserved in the presence of communication. This paper
largely supercedes our earlier note, "Communication
Can Destroy Common Learning."

We
study learning in a large class of complete information normal
form games. Players continually face new strategic situations
and must form beliefs by extrapolation from similar past
situations. The use of extrapolations in learning may generate
contagion of actions across games even if players learn only
from games with payoffs very close to the current ones.
Contagion may lead to unique long-run outcomes where
multiplicity would occur if players learned through repeatedly
playing the same game. The process of contagion through learning
is formally related to contagion in global games, although the
outcomes generally differ. We characterize the long-run outcomes
of learning in terms of iterated dominance in a related
incomplete information game with subjective priors, which
clarifies the connection to global games.

We
consider a cross-calibration test of predictions by
multiple potential experts in a stochastic environment which
tests whether each expert is calibrated conditional on the
predictions made by other experts. We show that this test is
good in the sense that a true expert – one informed of the true
distribution of the process – is guaranteed to pass the test no
matter what the other potential experts do, and false experts
will fail the test on all but a small (category one) set of true
distributions. Furthermore, even when there is no true expert
present, a test similar to cross-calibration cannot be
simultaneously manipulated by multiple false experts, but at the
cost of failing some true experts.